Masteries

Offense:
10

Defense:
20

Utility:
0

This is how I tend to play Akali. It's a hybrid build, obviously, because Akali is a hybrid champion. I focus on getting survivability first, and then damage because she is inherently a pretty squishy champion. I play her as a mix between AP and AD because I find that AP makes her a burst champion that has no sustainability after the initial hit. Any comments are appreciated, but please do not thumbs down this build without at least an explanation first. Give me the chance to make this build better and clarify things please!

Summoner Spells
Exhaust: I use exhaust because with Cripple it reduces the enemy's armor and magic resist, making you do a significant amount more damage since she hits with both simultaneously. It's useful for an early kill, or as a defense mechanism against someone like Jax or Ashe. Overall a good choice for Akali.

Ignite: Extra damage, healing reduction, and gives you 10 ability power when on cooldown. A great spell for Akali that's useful in many situations. Can be used to finish someone off, or you can use it on initiation as a means of getting extra AP.

Flash: I don't usually use Flash, but it is not to be overlooked. Useful to catch someone who is running, but Akali has Shadow Dance for that, so I generally don't use Flash.

Teleport: If you feel the need to quickly move around the map, go for it. I personally don't use it, but for some people Teleport is a must-have with any champion simply for the mobility it provides.

Any other summoner spells I don't usually bother with, since they don't have a whole lot of synergy with Akali.

Masteries
I like a 10/20/0 build for Akali. This gives more survivability, and still provides the necessary masteries from the offense tree to make Akali more deadly.

Archmage's Savvy: More ability power to make Akali's abilities hit harder, enough said.

Sorcery: Cooldown reduction so that you can hit more often with Mark of the Assassin, but mostly there so that you can get Archaic Knowledge.

Archaic Knowledge: 15% bonus spell penetration will make all of your damage abilities hit harder, as well as her passive gained from ability power.

Burning Embers: Free ability power while your ignite is on cooldown. Not as noticeable later in the game, but early on it's pretty significant.

Resistance: More magic resistance because Akali is squishy and will be targeted a lot because she is also melee.

Hardiness: Extra armor for the same reason as Resistance. Helps Akali's survivability.

Evasion: Still more survivability, of course!

Nimbleness: Your dodge is decent once you have Trinity force, so this will help you with a quick escape, or a quick chase to finish off that pesky Ashe or Master Yi who try to run.

Harden Skin: Helps you survive early on, and take less damage from minions. Overall a good one, even if the reduction is minimal.

Veteran's Scars: This is a big one. An extra 60 health early in the game is huge. That's an extra hit or two you can take from an enemy.

Ardor: Akali is based off of using her abilities and then hitting the opponent (Mark of the Assassin specifically). This mastery helps you with both of those aspects.

Runes
Greater Mark of Desolation x9: You are going to end up with a high amount of attack damage, so armor penetration will be very useful for your kills.

Greater Seal of Evasion x9: Helps with Nimbleness and provides you with more survivability to outlast your opponents.

Greater Glyph of Potency x9: The goal here is to get over 20 ability power at the start of the game so that you start with your AP-activated passive without items.

Greater Quintessence Potency x3: Between the Quintessences and Glyphs you will have 25 AP at the start of the game, making you hit a bit harder

Skills
Mark of the Assassin is your most devastating skill, which is why you level it up first.

Twilight Shroud is powerful for killing someone or escaping if used correctly. Can be used to hide and run, hide and gank, or even as a slow to keep your opponents from escaping alive.

Crescent Slash is good damage, and especially good for regaining some health with your passive.

Shadow Dance is your most awesome skill. Really increases your ability to chase, and can be used in a pinch to escape by dashing towards neutral monsters or enemy minions.

Skill Priorities:
R>Q>E>=W

*Note: W and E can be interchanged, depending on your play style and how the game is going. If you need a longer hide ability, level Twilight Shroud first. If you want more damage and more farming ability, level Crescent Slash first.

The Game
Start off with a Long Sword to get your second passive active. This and a healing potion are what you should be heading into the field with.

Akali is a good one for getting first blood because she can do so much burst between Exhaust, Ignite, Mark of the Assasin, and her passive abilities. If you have a good teammate this should be no problem

Beyond first blood, harass your opponents with Mark of the Assassin if they are melee, but otherwise use it for farming and health regeneration. With your passives active you shouldn't have too much trouble staying in the lane unless you are really getting pressured.

On your first return trip to your base, grab Boots of Swiftness to make yourself more mobile and dangerous, and if you have the money start building Sheen to later become Trinity Force.

Your next goal is to start killing minions and champions to farm up the money to finish Trinity Force. This will make you more deadly, and will increase your survivability. After Trinity Force make Rylai's for more survivability and a slow on all of your abilities.

Next you want to make a Guinsoo's Rageblade to stack up damage, attack speed, and ability power. A very synergistic item with Akali. Once you've finished these core items, build damage in whatever form you want. I like Bloodthirster and Black Cleaver, but Infinity Edge is a good option as well.

Both Golem and Lizard buffs are good for you, because Akali's abilities are low cooldown and expensive energy-wise, and she is designed as an assassin. She is an excellent farmer even without a lifesteal item due to her passive, so do not be afraid to go into the jungle early and often!

Once you've ended the laning phase, Akali is extremely deadly. You are survivable at this point, but make sure not to initiate. People will target you a lot because you are generally squishy and you are deadly, so let your team initiate first then dash in and wreak havoc.

Conclusions
This is just how I play Akali. If I'm getting very fed I'll sometimes grab Mejai's or SOTO, but I try not to rely on these items. The build isn't perfect, nor is it the only way to play Akali, it's just the way I like to play her. Any comments are more than welcome!

Again, if you are going to vote a -1, please leave a comment as to why prior to doing so so that I may fix the problem.